SEARCH · Search NASA

Results for “Corrected equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

NASA NTRS1984

An integrated software system for geometric correction of LANDSAT MSS imagery

A system for geometrically correcting LANDSAT MSS imagery includes all phases of processing, from receiving a raw computer compatible tape (CCT) to the generation of a corrected CCT (or UTM mosaic). The system comprises modules for: (1) control of the processing flow; (2) calculation of satellite ephemeris and attitude parameters, (3) generation of uncorrected files from raw CCT data; (4) creation, management and maintenance of a ground control point library; (5) determination of the image correction equations, using attitude and ephemeris parameters and existing ground control points; (6) generation of corrected LANDSAT file, using the equations determined beforehand; (7) union of LANDSAT scenes to produce and UTM mosaic; and (8) generation of output tape, in super-structure format.

Parada, N. D. J.↗

DOE OSTI2020

Improved reference system for the corrected rigid spheres equation of state model

The Corrected Rigid Spheres (CRIS) EOS model, developed from fluid perturbation theory using a hard sphere reference system, has been successfully used to calculate the EOS of many materials, including gases and metals. The radial distribution function (RDF) plays a pivotal role in choosing the sphere diameter, through a variational principle, as well as the thermodynamic response. Despite its success, the CRIS model has some shortcomings in that it predicts too large a temperature for liquid-vapor critical points, can break down at large compression, and is computationally expensive. In this paper, we first demonstrate that an improved analytic representation of the hard sphere RDF does not alleviate these issues. Relaxing the strict adherence of the RDF to hard spheres allows an accurate fit to the isotherms and vapor dome of the Lennard-Jones fluid using an arbitrary reference system. Second order correction are eliminated, limiting the breakdown at large compression and significantly reducing the computation cost. The transferrability of the new model to real systems is demonstrated on argon, with an improved vapor dome compared to the original CRIS model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2006

A New Empirical Thermospheric Density Model JB2006 using New Solar Indices

A new empirical atmospheric density model is developed using the CIRA72 (Jacchia 71) model as the basis for the diffusion equations. New solar indices based on orbit based sensor data are used for the solar irradiances in the extreme and far ultraviolet wavelengths. New exospheric temperature and semiannual density equations are employed to represent the major thermospheric density variations. Temperature correction equations are also developed for diurnal and latitudinal effects, and finally density correction factors are used for model corrections required at high altitude (1500-4000 km). The new model, Jacchia-Bowman 2006, is validated through comparisons of accurate daily density drag data previously computed for numerous satellite. For 400 km altitude the standard deviation of 16% for the standard Jacchia model is reduced to 10% for the new JB2006 model for periods of low geomagnetic storm activity.

Bowman, Bruce R.↗

NASA NTRS1981

Evaluation of HCMM data for assessing soil moisture and water table depth

Soil moisture in the 0-cm to 4-cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop in eastern South Dakota. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the soil temperature. Corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. Shallow alluvial aquifers were located with HCMM predawn data. After correcting the data for vegetation differences, equations were developed for predicting water table depths within the aquifer. A finite difference code simulating soil moisture and soil temperature shows that soils with different moisture profiles differed in soil temperatures in a well defined functional manner. A significant surface thermal anomaly was found to be associated with shallow water tables.

Moore, D. G.↗

NASA NTRS1994

Astrophysical Applications of Quantum Corrections to the Equation of State of a Plasma

The quantum electrodynamic correction to the equation of state of a plasma at finite temperature is applied to the areas of solar physics and cosmology. A previously neglected, purely quantum term in the correction is found to change the equation of state in the solar core by -0.37%, which is roughly estimated to decrease the calculated high energy neutrino flux by about 2.2%. We also show that a previous calculation of the effect of this correction on big bang nucleosynthesis is incomplete, and we estimate the correction to the primordial helium abundance Y to be Delta A= 1.4 x 10(exp -4). A physical explanation for the correction is found in terms of corrections to the dispersion relation of the electron, positron, and photon.

Heckler, Andrew F.↗

NASA NTRS1992

Multigrid calculation of internal flows in complex geometries

The development, validation, and application of a general purpose multigrid solution algorithm and computer program for the computation of elliptic flows in complex geometries is presented. This computer program combines several desirable features including a curvilinear coordinate system, collocated arrangement of the variables, and Full Multi-Grid/Full Approximation Scheme (FMG/FAS). Provisions are made for the inclusion of embedded obstacles and baffles inside the flow domain. The momentum and continuity equations are solved in a decoupled manner and a pressure corrective equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. Despite the computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence results in reduced overall CPU time. The numerical scheme and selected results of several validation flows are presented. Finally, the procedure is applied to study the flowfield in a side-inlet dump combustor and twin jet impingement from a simulated aircraft fuselage.

Smith, K. M.↗

NASA NTRS1995

Investigation of Convection and Pressure Treatment with Splitting Techniques

Treatment of convective and pressure fluxes in the Euler and Navier-Stokes equations using splitting formulas for convective velocity and pressure is investigated. Two schemes - controlled variation scheme (CVS) and advection upstream splitting method (AUSM) - are explored for their accuracy in resolving sharp gradients in flows involving moving or reflecting shock waves as well as a one-dimensional combusting flow with a strong heat release source term. For two-dimensional compressible flow computations, these two schemes are implemented in one of the pressure-based algorithms, whose very basis is the separate treatment of convective and pressure fluxes. For the convective fluxes in the momentum equations as well as the estimation of mass fluxes in the pressure correction equation (which is derived from the momentum and continuity equations) of the present algorithm, both first- and second-order (with minmod limiter) flux estimations are employed. Some issues resulting from the conventional use in pressure-based methods of a staggered grid, for the location of velocity components and pressure, are also addressed. Using the second-order fluxes, both CVS and AUSM type schemes exhibit sharp resolution. Overall, the combination of upwinding and splitting for the convective and pressure fluxes separately exhibits robust performance for a variety of flows and is particularly amenable for adoption in pressure-based methods.

Thakur, Siddharth↗

NASA NTRS1981

Evaluation of HCMM data for assessing soil moisture and water table depth

Data were analyzed for variations in eastern South Dakota. Soil moisture in the 0-4 cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop (% cover ranging from 30% to 90%) with an r squared = 0.81. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the 1-mm soil temperature, r squared = 0.88. The corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the 0-4 cm soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. HCMM data were used to estimate the soil moisture for four dates with an r squared = 0.55 after correction for crop conditions. Location of shallow alluvial aquifers could be accomplished with HCMM predawn data. After correction of HCMM day data for vegetation differences, equations were developed for predicting water table depths within the aquifer (r=0.8).

Moore, D. G.↗

NASA NTRS1988

Consistent boundary conditions for reduced Navier-Stokes (RNS) scheme applied to three-dimensional internal viscous flows

Three-dimensional internal viscous flow problems are presently addressed by a consistent and efficient set of boundary conditions for the multisweep space-marching, pressure-elliptic Reduced Navier-Stokes scheme. Since continuity is by this means directly satisfied at all points in the flow domain, the first-order momentum equations are directly solvable for pressure without the requirement for a Poisson pressure-correction equation. Incompressible flow solutions are obtained for straight and curved ducts of square cross section, in order to validate the procedure. Usefulness is demonstrated for internal flows with strong interactions, as would be found in turbomachine geometries.

Reddy, D. R.↗

NASA NTRS1989

Nonlinear strain-displacement relations and flexible multibody dynamics

Dynamics of chains of flexible bodies undergoing large rigid body motions, but small elastic deflections are considered. The role of nonlinear strain-displacement relations in the development of the motion equations correct to first order in elastic deflections is investigated. The general form of these equations linearized only in the small elastic deflections is presented, and the relative significance of various nonlinear terms is studied both analytically and through the use of the numerical simulations. Numerical simulations are performed for a two link chain constrained to move in the plane, subject to hinge torques. Each link is modeled as a thin beam. Slew maneuver simulation results are compared for models with and without properly modeled kinematics of deformation. The goal of this case study is to quantify the importance of the terms in the equations of motion which arise from the inclusion of nonlinear strain-displacement relations. It is concluded that unless the consistently linearized equations in elastic deflections and speeds are available and necessary, the inconsistently (prematurely) linearized equations should be replaced in all cases by ruthlessly linearized equations: equations in which all nonlinear terms involving the elastic deflections and speeds are ignored.

Padilla, Carlos E.↗

NASA NTRS1988

Consistent boundary conditions for Reduced Navier-Stokes (RNS) scheme applied to 3-dimensional internal viscous flows

A consistent and efficient set of boundary conditions is developed for the multi-sweep space-marching pressure-elliptic Reduced Navier-Stokes (RNS) scheme as applied for 3-D internal viscous flow problems. No-slip boundary conditions are directly imposed on the solid walls. There is no iteration procedure required in the cross plane to ensure mass conservation across each marching plane. The finite difference equations forming the coefficient matrix are ordered such that the surface normal velocity is specified on all the solid walls; unlike external flows, a pressure boundary condition in the cross plane is not required. Since continuity is directly satisfied at all points in the flow domain, the first order momentum equations can be solved directly for the pressure without the need for a Poisson pressure correction equation. The procedure developed herein can also be applied with periodic boundary conditions. The analysis is given for general compressible flows. Incompressible flow solutions are obtained, for straight and curved ducts of square cross section, to validate the procedure. These solutions are used to demonstrate the applicability of the RNS scheme, with the improved boundary conditions for internal flows with strong interaction, as would be encountered in ducts and turbomachinery geometries.

Reddy, D. R.↗

NASA NTRS1992

Arctic ice surface temperature retrieval from AVHRR thermal channels

The relationship between AVHRR thermal radiances and the surface (skin) temperature of Arctic snow-covered sea ice is examined through forward calculations of the radiative transfer equation, providing an ice/snow surface temperature retrieval algorithm for the central Arctic Basin. Temperature and humidity profiles with cloud observations collected on an ice island during 1986-1987 are used. Coefficients that correct for atmospheric attenuation are given for three Arctic clear sky 'seasons', as defined through statistical analysis of the daily profiles, for the NOAA 7, 9, and 11 satellites. Modeled directional snow emissivities, different in the two split-window (11 and 12 micron) channels, are used. While the sensor scan angle is included explicitly in the correction equation, its effect in the dry Arctic atmosphere is small, generally less than 0.1 K. Using the split-window channels and scan angle, the rms error in the estimated ice surface temperature is less than 0.1 K in all seasons. Inclusion channel 3(3.7 microns) during the winter decreases the rms error by less than 0.003

Key, J.↗

NASA NTRS1986

Estimation of absolute water surface temperature based on atmospherically corrected thermal infrared multispectral scanner digital data

Airborne remote sensing systems, as well as those on board Earth orbiting satellites, sample electromagnetic energy in discrete wavelength regions and convert the total energy sampled into data suitable for processing by digital computers. In general, however, the total amount of energy reaching a sensor system located at some distance from the target is composed not only of target related energy, but, in addition, contains a contribution originating from the atmosphere itself. Thus, some method must be devised for removing or at least minimizing the effects of the atmosphere. The LOWTRAN-6 Program was designed to estimate atmospheric transmittance and radiance for a given atmospheric path at moderate spectral resolution over an operational wavelength region from 0.25 to 28.5 microns. In order to compute the Thermal Infrared Multispectral Scanner (TIMS) digital values which were recorded in the absence of the atmosphere, the parameters derived from LOWTRAN-6 are used in a correction equation. The TIMS data were collected at 1:00 a.m. local time on November 21, 1983, over a recirculating cooling pond for a power plant in southeastern Mississippi. The TIMS data were analyzed before and after atmospheric corrections were applied using a band ratioing model to compute the absolute surface temperature of various points on the power plant cooling pond. The summarized results clearly demonstrate the desirability of applying atmospheric corrections.

Anderson, James E.↗

NASA NTRS1995

Reionization and its imprint of the cosmic microwave background

Early reionization changes the pattern of anisotropies expected in the cosmic microwave backgrond. To explore these changes, we derive from first principles the equations governing anisotropies, focusing on the interactions of photons with electrons. Vishniac (1987) claimed that second-order terms can be large in a reionized universe, so we derive equations correct to second order in the perturbations. There are many more second-order terms than were considered by Vishniac. To understand the basic physics involved, we present a simple analytic approximation to the first-order equation. Then, turning to the second order equation, we show that the Vishniac term is indeed the only important one. We also present numerical results for a variety of ionization histories (in a standard cold dark matter universe) and show quantitatively how the signal in several experiments depends on the ionization history. The most pronounced indication of a reionized universe would be seen in very small scale experiments; the expected signal in the Owens Valley experiment is smaller by a factor of order 10 if the last scattering surface is at a redshift z approximately = 100 as it would be if the universe were reionized very early. On slightly larger scales, the expected signal in a reionized universe is smaller than it would be with standard recombination, but only a factor of 2 or so. The signal is even smaller in these experiments in the intermediate case where some photons last scattered at the standard recombination epoch.

Dodelson, Scott↗

NASA NTRS1980

Error analysis and corrections to pupil diameter measurements with Langley Research Center's oculometer

Factors that can affect oculometer measurements of pupil diameter are: horizontal (azimuth) and vertical (elevation) viewing angle of the pilot; refraction of the eye and cornea; changes in distance of eye to camera; illumination intensity of light on the eye; and counting sensitivity of scan lines used to measure diameter, and output voltage. To estimate the accuracy of the measurements, an artificial eye was designed and a series of runs performed with the oculometer system. When refraction effects are included, results show that pupil diameter is a parabolic function of the azimuth angle similar to the cosine function predicted by theory: this error can be accounted for by using a correction equation, reducing the error from 6% to 1.5% of the actual diameter. Elevation angle and illumination effects were found to be negligible. The effects of counting sensitivity and output voltage can be calculated directly from system documentation. The overall accuracy of the unmodified system is about 6%. After correcting for the azimuth angle errors, the overall accuracy is approximately 2%.

Fulton, C. L.↗

NASA NTRS1972

Correction of satellite tracking data for an arbitrary tropospheric profile.

A procedure is given for deriving elevation-error and range-error correction equations in a form suitable for use in the rapid processing of satellite tracking data. The refractivity of the troposphere is assumed to have spherical symmetry, but may have any given profile that does not depart greatly from standard. When the procedure was tested for numerical accuracy by application to an exponential profile, the corrections calculated agreed with those obtained by ray tracing to 0.3% or better over a range of surface refractivity from 200 to 450 and a range of radiowave arrival angles from horizontal to vertical.

Marini, J. W.↗

NASA NTRS2017

Assessment of Terra MODIS On-Orbit Polarization Sensitivity Using Pseudoinvariant Desert Sites

The Moderate Resolution Imaging Spectroradiometer (MODIS) is currently flying on NASA's Earth Observing System Terra and Aqua satellites, launched in 1999 and 2002, respectively. MODIS reflective solar bands in the visible wavelength range are known to be sensitive to polarized light based on prelaunch polarization sensitivity tests. After about five years of on-orbit operations, it was discovered that the polarization sensitivity at short wavelengths had shown a noticeable increase. In this paper, we examine the impact of polarization on measured top-of-atmosphere (TOA) reflectance based on MODIS Collection-6 L1B over pseudo invariant desert sites. The standard polarization correction equation is used in combination with simulated at-sensor radiances using the second simulation of a satellite signal in the Solar Spectrum, Vector Radiative Transfer Code (6SV). We ignore the polarization contribution from the surface and a ratio approach is used for both 6SV-derived in put parameters and observed TOA reflectance. Results indicate that significant gain corrections up to 25% are required near the end of scan for the 412 and 443 nm bands. The polarization correction reduces the seasonal fluctuations in reflectance trends and mirror side ratios from 30% and 12% to 10% and 5%, respectively, for the two bands. Comparison of the effectiveness of the polarization correction with the results from the NASA Ocean Biology Processing Group shows a good agreement in the corrected reflectance trending results and their seasonal fluctuations.

Wu, Aisheng↗

NASA NTRS1991

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

Chen, C. P.↗